7 ms·
What makes solving IMO problems hard is usually the limits of human memory, pattern-matching, and search, not creativity. After all, these are problems that are
by gowld 2y ago
What makes solving IMO problems hard is usually the limits of human memory, pattern-matching, and search, not creativity. After all, these are problems that are already solved, and it is expected that many people can solve the problems in about 1 hour's time.
That makes it, in principle, similar or even easier than a champsionship-level chess move, which often take more than 1 hour for a professional human (with more training than an IMO high school student) to solve.
Another interesting concern is that when posing a problem to humans, it's fine to pose an "easy" brute-forceable problem, but humans, being slow brute-searchers, need to find more clever solutions. But if you give such a problem to a computer, it can trivialize it. So to test a computer, you need to pose non- easily-brute-forceable problems, which are harder for the computer than the others, but equally difficult for the humans as the other problems are.
- sebzim4500 2y agoOk but if you read the actual solutions they aren't a bizarre mess of brute force. They look like what a human would write if they were trying to come up with a formal proof (albeit it does some steps in a weird order).
- lupire 2y agoThe solutions aren't a bizarre mess of brute force. The search for the solutions is.
- knotthebest 2y agoThey are, though. I spoke to an author just yesterday. They did mostly use brute-force.
- snewman 2y agoWhy do you say these are problems that are already solved? Sure, they're often variations on existing themes, but the same is true for chess positions and, honestly, almost everything else in any field of human endeavor. Agreed that the absolute upper tier of chess players have trained longer and harder than most or all IMO contestants. Though I do wonder which (top-tier chess or the IMO) draws on a larger talent pool. To my understanding, a significant fraction of all high school students on Earth take some form of qualifying exam which can channel them into an IMO training program. And as far as the being amenable to brute force (relative difficulty for humans vs. computers): it seems that chess was comparatively easier for computers, IMO problems are comparatively easier for humans, and the game of Go is somewhere in between.
- okintheory 2y agoThese problems are literally already solved? Of course, the IMO problem designers make sure the problems have solutions before the use them. That's very different than math research, where it's not known in advance what the answer is, or even that there is good answer.
- snewman 2y agoI'm saying they weren't solved until the problem composer (created and) solved them. They're not, in general, problems for which solutions have been lying around. So "these are problems that are already solved" isn't introducing anything interesting or useful into the discussion. The post I was replying to was trying to draw a contrast with chess moves, presumably on the grounds that (after the opening) each position in a chess game is novel, but IMO problems are equally novel. It's true that IMO problems are vetted as being solvable, but that still doesn't really shed any information on how the difficulty of an IMO problem compares to the difficulty of chess play.